Finite Group DatabasebetaFinite Group Databasebeta| order | 4352 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #24408 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C17 · Schur multiplier (H2) = C26 |
| direct product | C17×#24409 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C2×C17 | #2410 |
| commutator, Frattini, cosocle | C22×C4 | C24×C17 |
| prime radical | C17×#3585 | C2 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C17 ◁ C22×C4×C17 ◁ G | |
1336 conjugacy classes of subgroups.
| minimal degree | μ(G) = 49 |
| transitive degree | μt(G) = 544 |
A minimal faithful permutation representation — 4 generators on 49 points:
(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17)(18,19)(20,28,31,24)(21,32)(22,26)(23,27)(25,34)(29,46,47,39)(30,44,37,40)(33,49,48,41)(35,45)(36,43)(38,42);(18,20)(19,24)(21,33)(22,31)(23,37)(25,41)(26,28)(27,44)(29,35)(30,36)(32,49)(34,48)(38,47)(39,42)(40,43)(45,46);(18,21)(19,25)(20,29)(22,34)(23,38)(24,39)(26,32)(27,45)(28,46)(30,48)(31,47)(33,37)(35,36)(40,49)(41,44)(42,43);(18,20)(19,24)(21,29)(22,31)(23,30)(25,39)(26,28)(27,40)(32,46)(33,35)(34,47)(36,37)(38,48)(41,42)(43,44)(45,49)680 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4352, 17397);